concepts · 11
- 01
The Perfect Eye: Perpendicular Bisectors
Find the exact centres for a symmetrical eye, prove with congruence that they give the perpendicular bisector, and construct it in three steps.
- 02
Right Angles Anywhere: At A Point, From Outside, And With A Rope
Draw a right angle at a point on a line or through a point outside it, and see how the Śulba-Sūtras did it with a rope.
- 03
Bisecting Angles: 45° And The Eight-Petalled Flower
Bisect any angle using SSS congruence, and use repeated bisection to build 45° designs like the eight-petalled flower.
- 04
Copying Angles And Drawing Parallel Lines
Copy any angle exactly using SSS congruence, and use that to construct a line parallel to a given line.
- 05
Arch Designs: Trefoil And Pointed Arches
Plan support lines for symmetrical arches, and construct trefoil and pointed arches with equal angles and equal lengths.
- 06
Regular Hexagons From Six Equilateral Triangles
Check whether angles fit around a point using the 360° total, and see why six equilateral triangles make a regular hexagon.
- 07
60°, 30° And 15° Angles, And The Six-Pointed Star
Construct 60° from an equilateral triangle, halve it to 30° and 15°, and build hexagons, stars and designs.
- 08
Tangram Puzzles: Seven Pieces, Many Shapes
Rearrange the seven tangram pieces into new shapes, reasoning about the pieces' sizes and angles.
- 09
Tiling Grids With Dominoes: Counting And Colouring
Decide whether a grid can be covered with 2 × 1 tiles by counting squares, and use chessboard colouring to prove some regions impossible.
- 10
Tiling The Whole Plane
Explain which regular polygons tile the plane using the angles at a corner, and meet tilings in art and in beehives.
- 11
Review: Constructions And Tilings
Check what you can now construct and explain, revise the key constructions, and solve mixed problems on constructions and tilings.